A numerical solver for least-squares sub-problems in 3D wavefield reconstruction inversion and related problem formulations

2019 ◽  
Author(s):  
Bas Peters ◽  
Felix J. Herrmann
Keyword(s):  
Least Squares ◽  
Related Problem ◽  
Problem Formulations ◽  
Numerical Solver

scholarly journals Optimal Polynomial Prediction Measures and Extremal Polynomial Growth

2020 ◽  
Author(s):  
L. Bos ◽  
N. Levenberg ◽  
J. Ortega-Cerdà
Keyword(s):  
Least Squares ◽  
Related Problem ◽  
Polynomial Growth ◽  
Compact Set ◽  
Extremal Polynomial ◽  
Real Polynomials ◽  
Optimal Polynomial

Abstract We show that the problem of finding the measure supported on a compact set $$K\subset \mathbb {C}$$ K ⊂ C such that the variance of the least squares predictor by polynomials of degree at most n at a point $$z_0\in \mathbb {C}^d\backslash K$$ z 0 ∈ C d \ K is a minimum is equivalent to the problem of finding the polynomial of degree at most n,  bounded by 1 on K,  with extremal growth at $$z_0.$$ z 0 . We use this to find the polynomials of extremal growth for $$[-1,1]\subset \mathbb {C}$$ [ - 1 , 1 ] ⊂ C at a purely imaginary point. The related problem on the extremal growth of real polynomials was studied by Erdős (Bull Am Math Soc 53:1169–1176, 1947).

scholarly journals Information content in data sets: A review of methods for interrogation and model comparison

2018 ◽  
Vol 26 (3) ◽  
pp. 423-452 ◽  
Author(s):  
H. Thomas Banks ◽  
Michele L. Joyner
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Information Content ◽  
Model Comparison ◽  
Model Parameters ◽  
Data Sets ◽  
Environmental Sciences ◽  
Amount Of Information ◽  
Problem Formulations

AbstractIn this review we discuss methodology to ascertain the amount of information in given data sets with respect to determination of model parameters with desired levels of uncertainty. We do this in the context of least squares (ordinary, weighted, iterative reweighted weighted or “generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in the biological and environmental sciences.

Heteroscedastic Methods for Performing All Pairwise Comparisons of Regression Lines Associated With J Independent Groups

Methodology ◽  
2015 ◽  
Vol 11 (3) ◽  
pp. 110-115 ◽  
Author(s):  
Rand R. Wilcox ◽  
Jinxia Ma
Keyword(s):  
Least Squares ◽  
Pairwise Comparisons ◽  
Simple Extension ◽  
Type I ◽  
Type I Errors ◽  
Well Elderly ◽  
Using Data

Abstract. The paper compares methods that allow both within group and between group heteroscedasticity when performing all pairwise comparisons of the least squares lines associated with J independent groups. The methods are based on simple extension of results derived by Johansen (1980) and Welch (1938) in conjunction with the HC3 and HC4 estimators. The probability of one or more Type I errors is controlled using the improvement on the Bonferroni method derived by Hochberg (1988) . Results are illustrated using data from the Well Elderly 2 study, which motivated this paper.

An fMRI study examining spatial navigation through a virtual environment: Partial least squares analysis

2005 ◽  
Author(s):  
Richard Mraz ◽  
Nancy J. Lobaugh ◽  
Genevieve Quintin ◽  
Konstantine K. Kakzanis ◽  
Simon J. Graham
Keyword(s):  
Least Squares ◽  
Virtual Environment ◽  
Partial Least Squares ◽  
Spatial Navigation ◽  
Partial Least Squares Analysis ◽  
Fmri Study

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

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